Researchers have recently focused on applying various nanoparticles/nanocomposites to improve the recovery factor from oil reservoirs. In this study, a new enhanced oil recovery agent, i.e., a ZnO–CuO (ZCO) nanocomposite, was synthesized, and its physicochemical properties are investigated by the scanning electron microscope, Fourier transform infrared spectrometer, Brunauer–Emmett–Teller, X-ray diffraction, and energy diffraction x-rays. The impact of ZCO and ZnO on interfacial tension, wettability change, and zeta potential tests has also been investigated under reservoir conditions. 0.1 weight percent (wt.%) of ZnO and ZCO in injection fluid, which minimizes contact angle and maximizes stability (i.e., minimum zeta potential), has been determined as the optimum concentration. The contact angle and zeta potential at this optimum concentration of ZnO and ZCO are 50.83°, 35.69° and −31.38, −35.65 mV, respectively. Then, the spontaneous imbibition using ZnO- and ZCO-based nanofluids with the optimum concentration is applied to monitor the recovery factor. The 22.5 day-long imbibition operation utilizing base fluid (without nanomaterials), ZnO, and ZCO retrieved 24.95%, 35.74%, and 52.01% of the oil, respectively. Overall, we concluded that injecting the ZCO-based nanofluids in carbonate porous media efficiently improves rocks and fluid parameters and enhances oil recovery.